In certain aspects, a method for training a model is disclosed. A model for measuring a geometric attribute of a hole structure in a semiconductor chip is provided by at least one processor. A plurality of training samples each including a pair of an optical spectrum signal and a reference signal corresponding to a same hole structure are obtained by the at least one processor. The reference signal is labeled with a labeled geometric attribute of the hole structure. An estimated geometric attribute of the hole structure is estimated using the model. A parameter of the model is adjusted based, at least in part, on a difference between the labeled geometric attribute and the estimated geometric attribute in each of the training samples by the at least one processor.

In certain aspects, a method for training a model is disclosed. A model for measuring a geometric attribute of a hole structure in a semiconductor chip is provided by at least one processor. A plurality of training samples each including a pair of an optical spectrum signal and a reference signal corresponding to a same hole structure are obtained by the at least one processor. The reference signal is labeled with a labeled geometric attribute of the hole structure. An estimated geometric attribute of the hole structure is estimated using the model. A parameter of the model is adjusted based, at least in part, on a difference between the labeled geometric attribute and the estimated geometric attribute in each of the training samples by the at least one processor.

Embodiments of systems and methods for measuring a geometric attribute of a hole structure in a semiconductor chip are disclosed. In an example, an optical spectrum signal corresponding to the hole structure in the semiconductor chip is received. The optical spectrum signal is characterized by one or more optical features. The geometric attribute of the hole structure is determined based, at least in part, on the optical features using a model. The model is trained from a plurality of training samples each including a pair of an optical spectrum signal and a labeled reference signal both corresponding to a same hole structure.

The rough bottom surface of a recessed feature partially obscured by an overlying structure is profiled interferometrically with acceptable precision using an objective with sufficiently large numerical aperture to illuminate the bottom under the obscuring structure. The light scattering produced by the roughness of the surface causes diffused light to return to the objective and yield reliable data fringes. Under such appropriate numerical-aperture and surface roughness conditions, the bottom surface of such recessed features can be profiled correctly simply by segmenting the correlograms produced by the scan and processing all fringes that correspond to the bottom surface elevation.

An inspection device includes: a first image unit that captures an image of an inspection object from a vertical direction; a plurality of dome-shaped reflector plates being arranged between the first image unit and the inspection object and having aperture parts on a side of the first image unit and a side of the inspection object, respectively; a plurality of annular light sources that illuminate the respective reflector plates; and apparatuses for inspection (second image unit and projection unit) that are provided outside of the reflector plates and are capable of capturing an image of the inspection object 12 or irradiating the inspection object with light. Optical axes of the apparatuses for inspection are arranged so as to pass through through-holes provided in the reflector plates.